Applied Mathematics

We study a class of discrete dynamical systems that is motivated by the generic structure of simulations. The systems consist of the following data: (a) a ®nite graph Y with vertex set f1Y F F F Y ng where each vertex has a binary state, (b) functions p i X F n 2 3 F n 2 and (c) an update ordering p. The functions p i update the binary state of vertex i as a function of the state of vertex i and its Y-neighbors and leave the states of all other vertices ®xed. The update ordering is a permutation of the Y-vertices. By composing the functions p i in the order given by p one obtains the sequential dynamical system (SDS DS): We derive a decomposition result, characterize invertible SDS DS and study ®xed points. In particular we analyse how many dierent SDS D S that can be obtained by reordering a given multiset of update functions and give a criterion for when one can derive concentration results on this number. Finally, some speci®c SDS DS are investigated.

This paper contains a survey of main results in the theory of invariant subspaces that have a direct or intermediate connection with the well-known list of problems in operator theory posed by Halmos in 1970. For most results we present brief proofs, schemes of proofs, or basic ideas of proofs. Bibliography: 124 titles.

The Vassiliev conjecture states that the Vassiliev invariants are dense in the space of all numerical link invariants in the sense that any link invariant is a pointwise limit of Vassiliev invariants. In this article, we prove that the Vassiliev conjecture holds in the case of the coefficients of the HOMFLY and the Kauffman polynomials. Contents 1 Reducing the problem: the weak Vassiliev conjecture 2 2 Approximation of the coefficients of the HOMFLYPT polynomial by Vassiliev invariants 3 2.1 Notations .

Submitted for the DFD13 Meeting of The American Physical Society von Neumann Stability Analysis of Pressure-Based Formulation of 1D and 2D Euler Equations SANTOSH KONANGI, URMILA GHIA, University of Cincinnati -The stability properties of a pressure-based scheme for the Euler equations are investigated, as such schemes are widely employed in commercial computational fluid dynamics codes. The published literature often focusses on model equations, and does not consider the solution scheme used in the parent code. The present study conducts a von Neumann stability analysis for a pressure-based, segregated scheme, SIMPLE (Semi-Implicit Method for Pressure-Linked Equations). The 1D and 2D Euler equations, closed by an "artificial" equation of state, are discretized using finite differences on a staggered grid, which permits equivalence to finite-volume discretization. As a first effort, first-order accurate spatial and temporal schemes are analyzed, to determine error amplification matrices, identify stable and unstable regimes, and predict practical stability limits in terms of the maximum allowable CFL number as a function of Mach number. The predictions are verified using the Riemann problem at several Mach numbers, and very good agreement is obtained between the predicted and the "numerically" observed CFL values. Hence, the present results should prove useful in guiding the stability of a simulation using the parent-code and the scheme tested here.

In this paper, an inverse compensator based on the Bouc-Wen model is used to reduce the effect of hysteresis on a piezoelectric micro-actuator. This compensator is used as an open loop controller which partially eliminates the system hysteresis effect. In the last step, in order to increase the reliability of the system and to achieve the desired goals, a H∞ robust controller is proposed in the presence of a compensator, to detect in the presence of modeling error and compensator error. At the end, simulation results are provided by MATLAB to demonstrate the effectiveness of the proposed control scheme. These results indicate that the proposed scheme provides a robust system performance and the tracking error reaches zero with acceptable accuracy.

In this paper, an inverse compensator based on the Bouc-Wen model is used to reduce the effect of hysteresis on a piezoelectric micro-actuator. This compensator is used as an open loop controller which partially eliminates the system hysteresis effect. In the last step, in order to increase the reliability of the system and to achieve the desired goals, a H∞ robust controller is proposed in the presence of a compensator, to detect in the presence of modeling error and compensator error. At the end, simulation results are provided by MATLAB to demonstrate the effectiveness of the proposed control scheme. These results indicate that the proposed scheme provides a robust system performance and the tracking error reaches zero with acceptable accuracy.

We present a novel topological proof of Goldbachs Conjecture, which states that every even integer greater than 2 can be expressed as the sum of two primes. By constructing a Prime Resonance Manifold M P , we define a resonance structure induced by prime numbers, where even integers arise as intersections of prime resonance trajectories. The proof leverages the dense tessellation of the manifold by prime resonance domains and entropydriven dynamics to ensure the existence of such intersections. TikZ illustrations visualize the manifold, resonance domains, and trajectory intersections, providing intuitive insight into the topological framework.

This study is an effort for measuring the entrepreneurial orientation of the students and its linkage with their entrepreneurial intention. The study is based on entrepreneurial dimensions such as innovativeness, need for achievements, opportunity recognition, risk-taking propensities, and entrepreneurship education. The study also used entrepreneurship education and gender as moderating variables. A 5-point Likert-type scale was designed by adapting the Individual Entrepreneurial Orientation measurement scale and Entrepreneurial Intention Questionnaire (EIQ). The authors postulated 7 hypotheses. Data analysis confirmed that underlying entrepreneurial dimensions have a positive correlation with students’ entrepreneurial intention. This paper concludes that entrepreneurial dimensions and proper delivery of entrepreneurship education will help the students in transforming their entrepreneurial intention into actual entrepreneurial action.

This study compares the three-factor model (F&F model) proposed by Eugene Fama and Kenneth French with Daniel and Titman’s Characteristics Model (D&T model) using the data of Indian stock returns for the period of 25 years from 1993 to 2018. Three-way sorting (3 × 2 × 2) of stocks based on the B/M ratio and size of the firms, and then by SMB, HML, or ex-ante β loadings, is formulated to design thirty-six portfolios. Regression and rolling regression are applied to the data under study. Results obtained by the F&F model, despite its shortcomings, are found more conclusive than the D&T model for distinguishing between characteristics and covariances for returns on Indian stock. This study favors the F&F model over the D&T model.

We study distributional solutions to the radially symmetric aggregation equation for power-law potentials. We show that distributions containing spherical shells form part of a basin of attraction in the space of solutions in the sense of ``shifting stability."" For spherical shell initial data, we prove the exponential convergence of solutions to equilibrium and construct some explicit solutions for specific ranges of attractive power. We further explore results concerning the evolution and equilibria for initial data formed from convex combinations of spherical shells.

Time-dependent dispersive shallow water waves in an unbounded domain are considered. The inÿnite domain is truncated via an artiÿcial boundary B, and a high-order non-re ecting boundary condition (NRBC) is imposed on B. Then the problem is solved by a ÿnite di erence scheme in the ÿnite domain bounded by B. The sequence of NRBCs proposed by Higdon is used. However, in contrast to the original low-order implementation of the Higdon conditions, a new scheme is devised which allows the easy use of a Higdon-type NRBC of any desired order. In addition, a procedure for the automatic choice of the parameters appearing in the NRBC is proposed. The performance of the scheme is demonstrated via a numerical example.

A class of three-point sixth-order multiple-root finders and the dynamics behind their extraneous fixed points are investigated by extending modified Newton-like methods with the introduction of the multivariate weight functions in the intermediate steps. The multivariate weight functions dependent on function-to-function ratios play a key role in constructing higher-order iterative methods. Extensive investigation of extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction. Numerical experiments applied to a number of test equations strongly support the underlying theory pursued in this paper. Relevant dynamics of the proposed methods is well presented with a variety of illustrative basins of attraction applied to various test polynomials.

We consider the construction of methods based on trigonometric polynomials for the initial value problems whose solutions are known to be periodic. It is assumed that the frequency w can be estimated in advance. The resulting methods depend on a parameter v = hw, where h is the step size, and reduce to classical multistep methods if v--, 0. Gautschi developed Adams and Strrmer type methods. In our paper we construct Nystrrm's and Milne-Simpson's type methods. Numerical experiments show that these methods are not sensitive to changes in w, but require the Jacobian matrix to have purely imaginary eigenvalues.

Several new methods for solving one nonlinear equation are developed. Most of the methods are of order three and they require the knowledge of f, f' and /". The methods will be compared to others in the literature. An extensive bibliography is given.

An optimal family of eighth-order multiple-zero finders and the dynamics behind their basins of attraction are proposed by considering modified Newton-type methods with multivariate weight functions. Extensive investigation of purely imaginary extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction. Numerical experiments strongly support the underlying theory pursued in this paper. An exploration of the relevant dynamics of the proposed methods is presented along with illustrative basins of attraction for various polynomials.

This paper introduces methods tailored especially for problems ' x whose solution behaves like e , where \ is complex. The shallow water equations with topography admit such solution. This paper complements the results of Pratt and others on exponential-fitted methods and those of Gautschi, Neta, van der Houwen and others on trigonometrically-f itted methods. 1 .

Two third order methods for finding multiple zeros of nonlinear functions are developed. One method is based on Chebyshev's third order scheme (for simple roots) and the other is a family based on a variant of Chebyshev's which does not require the second derivative. Two other more efficient methods of lower order are also given. These last two methods are variants of Chebyshev's and Osada's schemes. The informational efficiency of the methods is discussed. All these methods require the knowledge of the multiplicity.

In this paper, a practical analysis of stability by simulation for the effect of incorporating a Kalman estimator in the control loop of the inverted pendulum with a neurocontroller is presented. The neurocontroller is calculated by approximate optimal control, without considering the Kalman estimator in the loop following the Theorem of the separation. The results are compared with a time-varying linear controller, which in noiseless conditions in the state or in the measurement has an acceptable performance, but when it is under noise conditions its operation closes into a state space range more limited than the one proposed here.

Je remercie DIEU tout puissant de m'avoir donné la foie, le courage pour réaliser ce modeste travail et qui a mis dans mon chemin les bonnes personnes et m'a con…é aux bonnes mains. Je tiens en premier lieu à exprimer mes plus vifs remerciements à Madame K.Khelou… ma promotrice pour l'intéressant sujet qu'elle m'a proposé. Ainsi que pour son aide sa patience ses conseils et ses encouragements sa grande disponibilité et son ouverture d'esprit qui m'ont aidé à mener à bien ce travail. Je lui suis également reconnaissante pour la connaissance qu'elle ma accordée. Il m'est impossible de lui exprimer toute ma gratitude en seulement quelques lignes. J'adresse ma profonde gratitude et mes remerciements les plus vifs à Monsieur A. Berboucha, pour m'avoir fait l'honneur de présider le jury de cette soutenance. Je tiens à remercier également Madame S.Allili-Zahar qui a accepté d'examiner cet humble travail. Mes derniers et profonds remerciements vont à mes chers parents, frère et soeur, pour leur soutien et leur con…ance en moi, sans oublier mes amis et tous ceux qui ont servis, de près ou de loin pour achever ce travail. . i Je dédie ce modeste travail à: Mes chers parents qui étaient toujours attentifs, a¤ectueux et compréhensifs qui m'ont soutenu durant les laborieuses années de mes études, à qui je témoigne toute ma gratitude. Mon cher frère: houssem et ma cher soeur: naila. Mes très chers grand-parents. Ma chere grande famille: mes oncles et mes tantes, mes cousins et mes cousines. Toutes mes amies. Toute ma famille chacun par son nom. Tous les étudiants de notre département, en particulier notre promotion. I. X C(I; J) : l'espace des fonctions continue sur I à valeurs dans J: [a; b]): l'espace des fonctions u mesurables sur [a; b] et véri…ant b R a ju (t)j p dt < 1: Notations et conventions Si la réponse est a¢ rmative, on passe à d'autres questions: comment la solution peut-elle être construite ou approchée? Combien de solutions y a-t-il ? Quelle est la structure de l'ensemble de toutes les solutions? Dans ce mémoire, on s'intéresse notamment à l'étude d'existence de points …xes positifs d'une contraction stricte d'ensembles en prolongeant le concept de l'indice du point …xe dé…ni pour les applications complètement continues à des classes d'applications plus larges (les contractions strictes d'ensembles et les applications condensantes). Une contraction stricte d'ensemble est une application telle que l'image de tout ensemble borné est en un certain sens plus compacte que l'ensemble lui-même. Le degré de non-compacité est mesuré à l'aide d'une fonction appelée mesure de non-compacité. Le premier qui a considéré la mesure de non-compacité d'un sous-ensemble A d'un espace métrique est K. Kuratowski en 1930. Dans les années cinquante, G. Darbo, A. Furi, M.A. Krasnosel'skii et autres ont appliqué di¤érentes mesures de non-compacité dans les théories du point …xe, des applications linéaires et des équations di¤érentielles et intégrales. Ce mémoire comprend trois chapitres: Le premier chapitre contient un ensemble de dé…nitions et de résultats qui nous seront indispensables à la compréhension de la suite de cette étude. Ces résultats concernent essentiellement les notions suivantes: la mesure de non-compacité de Kuratowski, les contractions strictes d'ensembles, les applications condensantes et les cônes. Dans le deuxième chapitre, nous présentons quelques théorèmes du point …xe sur les cônes pour les contractions strictes d'ensembles qui entraînent l'existence ou la multiplicité d'un point …xe positif. La première section de ce chapitre est consacrée à la dé…nition de l'indice du point …xe pour une contraction stricte d'ensembles. Dans la deuxième section, nous rassemblons quelques lemmes fondamentaux utiles pour la suite de ce travail, puis nous donnons quelques développements récents du célèbre théorème de Krasnosel'skii, établi en 1960 et développé par la suite par beaucoup d'auteurs, on peut citer les travaux de Guo ([14],1988), Avery et Anderson ([3], 2002), Avery, Anderson et Krueger ([4], 2006). Ces récents développements sont dû à Sun ([26], 1986), Meiqiang, Zhang et Weigao ([20], 2010) pour les contractions strictes d'ensembles. Dans la troisième section, nous nous intéressons à l'existence des points …xes multiples d'une contraction stricte d'ensembles dé…nie sur un cône dans un espace de Banach ordonné. Plus précisément, nous présentons

The mathematical modeling of solar cell device is used to demonstrate the equivalent circuit of single-diode solar cell model operating under environmental conditions. In this work, bisection (BM) and secant (SM) Methods currently exists to demonstrate the non-linear electrical behavior of this device. The proposed method is tested in order to solve non-linear equation of PV cell with various values of load resistance are characterized. Comparisons between these numerical examples have been compared. The main idea of the present work is to calculate the PV parameters numerically using different methods with the comparison between them. The results showed that secant method is the best because it has least iteration to obtain the optimal values of the PV parameters.

Many numerical approaches have been proposed for solving a non-linear equation (PV cell model). In this paper, Inverse Quadratic Interpolation method using initial value x_0 is implemented in MATLAB for solving the problem of this design. Comparisons the results obtained in terms of number of iterations and absolute error show promising application of the proposed method for solving nonlinear examples.

The basic motivation of the present work is to apply the Predictor-Corrector [type 2] algorithm to perform the steps in Newton&#39;s and modified Newton&#39;s methods for approximating the solution of nonlinear equation of single diode model for a solar cell. A simple starting point for the iterative solutions is proposed. Some numerical applications are depicted and show that eight iterations are required to acquire approximate solutions, which are found to be sufficient, accurate, and efficient.

In the present work, two iterative techniques have been displayed in order to solve non-linear equation. These two techniques are free from second derivative and per evaluation; they require five and six iterations with a first derivative of the function. Analysis of the PV model has been studied in term of function evaluations appears that the proposed technique is superior. It is practical interest is investigated by some numerical examples.

In the present paper, the properties of Boubaker orthonormal polynomials are used to construct new Boubaker wavelet orthonormal functions which are continuous on the interval [0, 1). Then, a Boubaker wavelet orthonormal operational matrix of the derivative is obtained with the new general procedure. The matrix elements can be expressed in a simple form that reduces the computational complexity. The collocation method of the Boubaker orthonormal wavelet functions together with the application of the derived operational matrix of the derivative are then utilized to transform the higher-order integro-differential equation into a solution of linear algebraic equations. As a result, the solution of the original problem reduces to the solution of a linear system of algebraic equations and can be sufficiently solved by an approximate technique. The main advantage of the suggested method is that the orthonormality property greatly simplifies the original problem and leads to easy calculatio...

Modified second kind Chebyshev polynomials for solving higher order differential equations are presented in this paper. This technique, along with some new properties of such polynomials, will reduce the original differential equation problem to the solution of algebraic equations with a straightforward and computational digital computer. Some illustrative examples are included. The modified second kind Chebyshev polynomial is calculated using only a small number of the modified second kind Chebyshev polynomials, which leads to attractive results.

In this paper, we propose an efficient approximate indirect method for solving problems in calculus of variational. First, we introduce orthonormal Boubaker polynomials along with their important properties. These properties are employed to derive a general expansion of their operational matrices of derivation and integration along with a product operational matrix. The operational matrices are then used to approximate the solution. Finally, such approximations are substituted in the functional and necessary optimal condition, which then transform the variational problem under consideration into an algebraic system. Examples illustrate the validity and accuracy of the presented method.

We experimentally study the information aggregation process in a laboratory financial market when a public signal is released. The public disclosure crowds out information demand and reduces price informativeness. The latter effect is primarily caused by the overweighting of public information into prices. We are the first in providing evidence that strategic pricing concerns trigger the overweighting effect and the consequent market overreaction to public disclosures. From an economic policy perspective, we give support that, when deciding their communication strategy, the regulator can mitigate the market overreaction by properly setting the level of information transparency.

We present a spectral method for one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, including ones with irrational order, multiple fractional orders, non-trivial variable coefficients, and initial-boundary conditions. The method uses an orthogonal basis that we refer to as Jacobi fractional polynomials, which are obtained from an appropriate change of variable in weighted classical Jacobi polynomials. New algorithms for building the matrices used to represent fractional integration operators are presented and compared. Even though these algorithms are unstable and require the use of high-precision computations, the spectral method nonetheless yields well-conditioned linear systems and is therefore stable and efficient. For time-fractional heat and wave equations, we show that our method (which is not sparse but uses an orthogonal basis) outperforms a sparse spectral method (which uses a basis t...

We present a spectral method for one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, including ones with irrational order, multiple fractional orders, non-trivial variable coefficients, and initial-boundary conditions. The method uses an orthogonal basis that we refer to as Jacobi fractional polynomials, which are obtained from an appropriate change of variable in weighted classical Jacobi polynomials. New algorithms for building the matrices used to represent fractional integration operators are presented and compared. Even though these algorithms are unstable and require the use of high-precision computations, the spectral method nonetheless yields wellconditioned linear systems and is therefore stable and efficient. For time-fractional heat and wave equations, we show that our method (which is not sparse but uses an orthogonal basis) outperforms a sparse spectral method (which uses a basis that is not orthogonal) due to its superior stability.

The most common monitoring method of metal–oxide surge arrester is based on leakage current measurement, particularly, the component of resistive leakage current. Nowadays, there are several analytical methods used to extract the resistive leakage current. These analytical methods need both current and voltage signals. However, in fact, electrical system voltage contains harmonics and because of these harmonics, it may affect the accuracy of resistive leakage current extraction methods in different ways. The calculated results may be in error or incorrect. It can lead to erroneous evaluation or fault assessment. This paper attempts to clarify the influence of harmonics voltage on current extraction methods. Eventually, the results can be utilized for choosing the extraction method which is suitable for the measured data or limitation of each algorithm.

Effective early detection of forest fires can be achieved by specialised systems of tower-mounted cameras. Foresters and locals with intimate knowledge of the terrain traditionally plan the tower site locationswithout the aid of computational optimisation tools. However, such knowledge and expertise may not be available to system planners when entering vast new territories. The process of selecting multiple tower sites from a large number of potential site locations with the aim of maximising system visibility of smoke above a prescribed region is a complex combinatorial optimisation problem. We present two recent applications of novel site-selection frameworks for tower-mounted camera-based wildfire detection systems (CWDS), which have been under development with guidance from experts from the South African-developed ForestWatch wildfire detection system. A novel single-site search framework determined alternatives for thirteen proposed sites in South Africa's Mpumalanga province, of which 6 alternatives were chosen over the initially proposed sites. The system-site selection framework was showcased in determining a four-camera CWDS layout in South Africa's Southern Capedrastically improving on the detection capability of the layout initially proposed by technical experts.

STRIKE is a diagnostic calorimeter composed of 16 CFC tiles with unidirectional properties used to study the beams of particles generated in the SPIDER experiment. Two thermal cameras will be used to analyze the temperature of the tiles and reconstruct the bidimensional flux of energy striking the calorimeter. Most of the conventional methods used to evaluate the inverse heat flux are unbearably time consuming; since the objective is having a tool for heat flux evaluation for STRIKE real time operation, the need to have a ready-to-go instrument to understand the beam condition becomes stringent. For this reason a neural network was chosen to perform this analysis. During the thesis work an existing convolutional neural network was optimized to retrieve the parameters of the beam from the thermographic images. In particular, starting from a network able to determine the position and the radius of a singular circular shape on a noiseless background, the possibility to recognize the po...

In this paper, we analyze the behavior of stochastic approximation schemes with set-valued maps in the absence of a stability guarantee. We prove that after a large number of iterations if the stochastic approximation process enters the domain of attraction of an attracting set it gets locked into the attracting set with high probability. We demonstrate that the above result is an effective instrument for analyzing stochastic approximation schemes in the absence of a stability guarantee, by using it obtain an alternate criteria for convergence in the presence of a locally attracting set for the mean field and by using it to show that a feedback mechanism, which involves resetting the iterates at regular time intervals, stabilizes the scheme when the mean field possesses a globally attracting set, thereby guaranteeing convergence. The results in this paper build on the works of V.S. Borkar, C. Andrieu and H. F. Chen , by allowing for the presence of set-valued drift functions.

In this paper, we consider the stochastic iterative counterpart of the value iteration scheme wherein only noisy and possibly biased approximations of the Bellman operator are available. We call this counterpart as the approximate value iteration (AVI) scheme. Neural networks are often used as function approximators, in order to counter Bellman's curse of dimensionality. In this paper, they are used to approximate the Bellman operator. Since neural networks are typically trained using sample data, errors and biases may be introduced. The design of AVI accounts for implementations with biased approximations of the Bellman operator and sampling errors. We present verifiable sufficient conditions under which AVI is stable (almost surely bounded) and converges to a fixed point of the approximate Bellman operator. To ensure the stability of AVI, we present three different yet related sets of sufficient conditions that are based on the existence of an appropriate Lyapunov function. These Lyapunov function based conditions are easily verifiable and new to the literature. The verifiability is enhanced by the fact that a recipe for the construction of the necessary Lyapunov function is also provided. We also show that the stability analysis of AVI can be readily extended to the general case of set-valued stochastic approximations. Finally, we show that AVI can also be used in more general circumstances, i.e., for finding fixed points of contractive set-valued maps.

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Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.

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We analyze a decentralized trading process in a basic labor market where heterogeneous firms and workers meet directly and randomly, and negotiate salaries with each other over time. Firms and workers may not have a complete picture of the entire market and can thus behave myopically in the process. Our main result establishes that, starting from an arbitrary initial market state, there exists a finite sequence of successive myopic (firm-worker) pair improvements, or bilateral trades, leading to a stable matching between firms and workers with a scheme of competitive salary offers. An important implication of this result is that a general random process where every possible bilateral trade is chosen with a positive probability converges with probability one to a competitive equilibrium of the market.

We study a test statistic based on the integrated squared difference between a kernel estimator of the copula density and a kernel smoothed estimator of the parametric copula density. We show for fixed smoothing parameters that the test is consistent and that the asymptotic properties are driven by a U -statistic of order 4 with degeneracy of order 1. For practical implementation we suggest to compute the critical values through a semiparametric bootstrap. Monte Carlo results show that the bootstrap procedure performs well in small samples. In particular size and power are less sensitive to smoothing parameter choice than they are under the asymptotic approximation obtained for a vanishing bandwidth.

In this paper, we investigated the notion of a linear Diophantine fuzzy set (LDFS) by using the concept of a score function to build the LDF-score left (right) ideals and LDF-score (0,2)-ideals in an AG-groupoid. We used these newly developed LDF-score ideals to characterize an AG-groupoid. We then use the proposed structure in multiattribute decision-making by considering bridge design selection and artificial intelligence-based chatbot selection.

The aim of this article is to implement the Generalized Modified Adomian Decomposition Method to compute the semi-numerical solution of the linear system of intuitionistic fuzzy initial value problems. Here, we consider the initial values as generalized trapezoidal intuitionistic fuzzy numbers. The technique is applied to brine tanks problem and coupled mass spring systems.Theoretically, different approaches to solving a system of generalized trapezoidal intuitionistic fuzzy differential equations are discussed in this study under the presumption that the coefficients of the system of the differential equations are associated to generalized trapezoidal intuitionistic fuzzy numbers. The approximate results are compared with exact solutions which shows good efficiency. The corresponding graphs at different levels of uncertainty show the example's numerical outcomes. The graphical representations further demonstrate the effectiveness and accuracy of the proposed method in comparison to existing semi-numerical methods in the literature. INDEX TERMS Fuzzy set, fuzzy number, generalized trapezoidal intuitionistic fuzzy number, system of fuzzy differential equation, analytical technique, engineering applications.